Movement-based interfaces assume that their users move. Users have to perform exercises, they have to dance, they have to golf or football, or they want to train particular bodily skills. Many examples of those interfaces exist, sometimes asking for subtle interaction between user and interface and sometimes asking for 'brute force' interaction between user and interface. Often these interfaces mediate between players of a game. Obviously, one of the players may be a virtual human. We embed this interface research in ambient intelligence and entertainment computing research, and the interfaces we consider are not only mediating, but they also 'add' intelligence to the interaction. Intelligent movement-based interfaces, being able to know and learn about their users, should also be able to provide means to keep their users engaged in the interaction. Issues that will be discussed in this chapter are 'flow' and 'immersion' for movement-based interfaces and we look at the possible role of interaction synchrony to measure and support engagement.